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arXiv · 2302.08318

On blowups of vorticity for the homogeneous Euler equation

B. G. Konopelchenko·G. Ortenzi
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Abstract

Blowups of vorticity for the three- and two- dimensional homogeneous Euler equations are studied. Two regimes of approaching a blowup points, respectively, with variable or fixed time are analysed. It is shown that in the $n$-dimensional ($n=2,3$) generic case the blowups of degrees $1,..,n$ at the variable time regime and of degrees $1/2,..,(n+1)/(n+2)$ at the fixed time regime may exist. Particular situations when the vorticity blows while the direction of the vorticity vector is concentrated in one or two directions are realisable.

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BibTeXRIS

B. G. Konopelchenko, G. Ortenzi. 2023-02-16. On blowups of vorticity for the homogeneous Euler equation. https://arxiv.org/abs/2302.08318

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